In the last several decades, personal computers and other consumer computing devices, such has hand-held devices and smart phones, have become ubiquitous among the general public. As the proliferation of personal computers and other computing devices became prevalent, the usefulness of the computers and other computing devices was increased by interconnected communications between different computers/computing, devices via various electronic networking communications systems. With the advent of the publicly accessible Internet and the establishment of the World Wide Web (WWW) for common communications between computers and/or other computing devices on the Internet, it became common for private identification and financial information to be transferred over the publicly accessible Internet. To ensure that the private information is not accessed by parties that are not intended to be privy to the private information, various encryption techniques have been applied to the private data being transferred over the Internet. As data storage has become accessible over networking technologies, including over the publicly accessible Internet, it has also become prudent to store sensitive data in an encrypted format.
Modern encryption employs mathematical techniques that manipulate positive integers or binary bits. Asymmetric encryption, such as RSA (Rivest-Shamir-Adleman), relies on number theoretic one-way functions that are predictably difficult to factor and can be made more difficult with an ever increasing size of the encryption keys. Symmetric encryption, such as DES (Data Encryption Standard) and AES (Advanced Encryption Standard), uses bit manipulations within registers to shuffle the cryptotext to increase “diffusion” as well as register based operations with a shared key to increase “confusion.” Diffusion and confusion are measures for the increase in statistical entropy on the data payload being transmitted. The concepts of diffusion and confusion in encryption are normally attributed as first being identified by Claude Shannon in the 1940s. Diffusion is generally thought of as complicating the mathematical process of generating unencrypted (plain text) data from the encrypted (cryptotext) data, thus, making it difficult to discover the encryption key of the encryption process by spreading the influence of each piece of the unencrypted (plain) data across several pieces of the encrypted (cryptotext) data. Consequently, an encryption system that has a high degree of diffusion will typically change several characters of the encrypted (cryptotext) data for the change of a single character in the unencrypted (plain) data making it difficult for an attacker to identify changes in the unencrypted (plain) data. Confusion is generally thought of as obscuring the relationship between the unencrypted (plain) data and the encrypted (cryptotext) data. Accordingly, an encryption system that has a high degree of confusion would entail a process that drastically changes the unencrypted (plain) data into the encrypted (cryptotext) data in a way that, even when an attacker knows the operation of the encryption method (such as the public standards of RSA, DES, and/or AES), it is still difficult to deduce the encryption key.